A semi-mechanistic exposure-response model to assess the effects of verinurad, a potent URAT1 inhibitor, on serum and urine uric acid in patients with hyperuricemia-associated diseases.

Verinurad, a uric acid transporter 1 (URAT1) inhibitor, lowers serum uric acid by promoting its urinary excretion. Co-administration with a xanthine oxidase inhibitor (XOI) to simultaneously reduce uric acid production rate reduces the potential for renal tubular precipitation of uric acid, which can lead to acute kidney injury. The combination is currently in development for chronic kidney disease and heart failure. The aim of this work was to apply and extend a previously developed semi-mechanistic exposure-response model for uric acid kinetics to include between-subject variability to verinurad and its combinations with XOIs, and to provide predictions to support future treatment strategies. The model was developed using data from 12 clinical studies from a total of 434 individuals, including healthy volunteers, patients with hyperuricemia, and renally impaired subjects. The model described the data well, taking into account the impact of various patient characteristics such as renal function, baseline fractional excretion of uric acid, and race. The potencies (EC50s) of verinurad (reducing uric acid reuptake), febuxostat (reducing uric acid production), and oxypurinol (reducing uric acid production) were: 29, 128, and 13,030 ng/mL, respectively. For verinurad, symptomatic hyperuricemic (gout) subjects showed a higher EC50 compared with healthy volunteers (37 ng/mL versus 29 ng/mL); while no significant difference was found for asymptomatic hyperuricemic patients. Simulations based on the uric acid model were performed to assess dose-response of verinurad in combination with XOI, and to investigate the impact of covariates. The simulations demonstrated application of the model to support dose selection for verinurad.

Using sensitivity equations for computing gradients of the FOCE and FOCEI approximations to the population likelihood.

The first order conditional estimation (FOCE) method is still one of the parameter estimation workhorses for nonlinear mixed effects (NLME) modeling used in population pharmacokinetics and pharmacodynamics. However, because this method involves two nested levels of optimizations, with respect to the empirical Bayes estimates and the population parameters, FOCE may be numerically unstable and have long run times, issues which are most apparent for models requiring numerical integration of differential equations. We propose an alternative implementation of the FOCE method, and the related FOCEI, for parameter estimation in NLME models. Instead of obtaining the gradients needed for the two levels of quasi-Newton optimizations from the standard finite difference approximation, gradients are computed using so called sensitivity equations. The advantages of this approach were demonstrated using different versions of a pharmacokinetic model defined by nonlinear differential equations. We show that both the accuracy and precision of gradients can be improved extensively, which will increase the chances of a successfully converging parameter estimation. We also show that the proposed approach can lead to markedly reduced computational times. The accumulated effect of the novel gradient computations ranged from a 10-fold decrease in run times for the least complex model when comparing to forward finite differences, to a substantial 100-fold decrease for the most complex model when comparing to central finite differences. Considering the use of finite differences in for instance NONMEM and Phoenix NLME, our results suggests that significant improvements in the execution of FOCE are possible and that the approach of sensitivity equations should be carefully considered for both levels of optimization.

A stochastic mixed effects model to assess treatment effects and fluctuations in home-measured peak expiratory flow and the association with exacerbation risk in asthma.

Home-based measures of lung function, inflammation, symptoms, and medication use are frequently collected in respiratory clinical trials. However, new statistical approaches are needed to make better use of the information contained in these data-rich variables. In this work, we use data from two phase III asthma clinical trials demonstrating the benefit of benralizumab treatment to develop a novel longitudinal mixed effects model of peak expiratory flow (PEF), a lung function measure easily captured at home using a hand-held device. The model is based on an extension of the mixed effects modeling framework to incorporate stochastic differential equations and allows for quantification of several statistical properties of a patient's PEF data: the longitudinal trend, long-term fluctuations, and day-to-day variability. These properties are compared between treatment groups and related to a patient's exacerbation risk using a repeated time-to-event model. The mixed effects model adequately described the observed data from the two clinical trials, and model parameters were accurately estimated. Benralizumab treatment was shown to improve a patient's average PEF level and reduce long-term fluctuations. Both of these effects were shown to be associated with a lower exacerbation risk. The day-to-day variability was neither significantly affected by treatment nor associated with exacerbation risk. Our work shows the potential of a stochastic model-based analysis of home-based lung function measures to support better estimation and understanding of treatment effects and disease stability. The proposed analysis can serve as a complement to descriptive statistics of home-based measures in the reporting of respiratory clinical trials.

Higher Febuxostat Exposure Observed in Asian Compared with Caucasian Subjects Independent of Bodyweight.

BACKGROUND AND OBJECTIVE: Febuxostat is a xanthine oxidase inhibitor indicated for gout and hyperuricemia. This work investigates potential clinically relevant covariates for febuxostat pharmacokinetics with a special focus on Asian race and bodyweight. METHODS: Febuxostat plasma concentrations from 141 male subjects were obtained from two phase II studies in patients with hyperuricemia/gout (NCT02246673, NCT02317861) and one study in healthy volunteers (NCT01883167). Subjects were administered febuxostat oral doses from 10 to 80 mg. The pharmacokinetics of febuxostat was analyzed using non-linear mixed-effects modeling as implemented in NONMEM 7.3.0. The dataset consisted of racially diverse subjects, 40% being Japanese, 10% of unknown Asian origin, 39% Caucasian, and 10% Black. Most subjects (n = 92, 63%) had normal creatinine clearance (90 mL/min), while 52 subjects (36%) had mild renal impairment (creatinine clearance > 60 to < 90) at baseline. The effect of disease state, body weight, and creatinine clearance on febuxostat pharmacokinetics was investigated using stepwise covariate modeling. RESULTS: Febuxostat pharmacokinetics was well described by a two-compartment disposition model. Asian race was the only covariate resulting in a potentially clinically important increase in febuxostat area under the curve (1.64-fold, 90% confidence interval 1.48-1.79) compared with Caucasian individuals. The difference in body weight between Asian and Caucasian subjects did not explain the difference in febuxostat exposure. Absorption was modeled as a sequential zero- to first-order process with lag-time. CONCLUSIONS: In this pooled analysis of three studies, we show that Asian individuals have a 1.64-fold higher febuxostat exposure than Caucasians, independent of bodyweight or other investigated covariates. These findings may be of importance when selecting starting febuxostat doses in Asian patients.

Estimation of Equipotent Doses for Anti-Inflammatory Effects of Prednisolone and AZD9567, an Oral Selective Nonsteroidal Glucocorticoid Receptor Modulator.

AZD9567 is a potent and selective nonsteroidal oral glucocorticoid receptor modulator. It is developed as an anti-inflammatory drug with improved safety profile compared with steroids like prednisolone. Throughout the clinical development of AZD9567, dose selection and data interpretation require a method for determining doses with the same anti-inflammatory effect as prednisolone. Equipotent doses of AZD9567 and prednisolone were defined by the same average inhibition of TNFα release, a biomarker of anti-inflammatory effect, measured in a lipopolysaccharide-stimulated whole blood ex vivo assay. Based on pharmacokinetic-pharmacodynamic models, TNFα dose-response relationships for AZD9567 and prednisolone were established. A comparison of the dose-response curves enabled estimation of an equipotency relationship. Specifically, 20 mg prednisolone was estimated to be equipotent to 40 mg AZD9567 (95% confidence interval: 29-54 mg). Static concentration-response analyses showed that the relative potencies for inhibition of TNFα release of AZD9567 and prednisolone were well aligned with several other pro-inflammatory cytokines.

Effects of a selective glucocorticoid receptor modulator (AZD9567) versus prednisolone in healthy volunteers: two phase 1, single-blind, randomised controlled trials.

BACKGROUND: Glucocorticoids are highly effective and widely used anti-inflammatory drugs, but their use is limited by serious side-effects, including glucocorticoid-induced hyperglycaemia and diabetes. AZD9567 is a non-steroidal, selective glucocorticoid receptor modulator that aims to reduce side-effects. We aimed to assess the safety, tolerability, and pharmacokinetics of AZD9567 in healthy volunteers. METHODS: Two phase 1 clinical studies were done. First, a randomised, placebo-controlled, single-blind, single-ascending dose study was done in healthy men who received single oral doses of AZD9567 2 mg, 10 mg, 20 mg, 40 mg, 80 mg, 100 mg, 125 mg, or 155 mg, or prednisolone 60 mg (n=8 per dose group, randomly assigned [6:2] to receive active drug or placebo). Second, a randomised, active-controlled, single-blind, multiple-ascending dose study was done, in which men and women received oral AZD9567 or prednisolone once daily for 5 days. One cohort of volunteers with prediabetes received AZD9567 10 mg (n=7) or prednisolone 20 mg (n=2). All other cohorts comprised healthy volunteers, receiving AZD9567 20 mg, 40 mg, 80 mg, or 125 mg (n=7 per dose group), or prednisolone 5 mg (n=13), 20 mg (n=16), or 40 mg (n=13). Participants and study centre staff were masked to treatment assignment for each cohort, although data were unmasked for safety review between cohorts. The primary outcome of the single-ascending dose study was the safety, tolerability, and pharmacokinetics of single ascending doses of AZD9567; for the multiple-ascending dose study it was the safety and tolerability of AZD9567 following multiple ascending doses. As a secondary outcome, effects on glycaemic control were ascertained with oral glucose tolerance tests (OGTTs) done at baseline and on day 1 of the single-ascending dose study, and at baseline and on day 4 of the multiple-ascending dose study. These trials are registered at ClinicalTrials.gov, NCT02512575 and NCT02760316. FINDINGS: In the single-ascending dose study, between Nov 18, 2015, and Sept 26, 2016, 72 healthy white men were enrolled, and all completed the study. In the multiple-ascending dose study, between May 2, 2016, and Sept 13, 2017, 77 predominantly white male volunteers (including nine individuals with prediabetes and eight women) were enrolled and 75 completed the study. All doses of AZD9567 and prednisolone were well tolerated, with no serious adverse events or events suggesting adrenal insufficiency. In the single-ascending dose study, nine adverse events of mild intensity were reported (five with AZD9567 and four with placebo); no adverse event was reported by more than one person. In the multiple-ascending dose study, 44 adverse events of mild or moderate intensity were reported (18 with AZD9567 and 26 with prednisolone). The most common were headache and micturition. Apparent clearance, volume of distribution, and half-life of AZD9567 were consistent across doses and for single versus repeated dosing. In the multiple-ascending dose study, OGTTs showed no significant difference with AZD9567 doses up to 80 mg compared with prednisolone 5 mg in glucose area under the curve from 0 h to 4 h post-OGTT (AUC0-4h) from baseline to day 4; the increase in glucose AUC0-4h from baseline to day 4 was significantly lower with all AZD9567 doses versus prednisolone 20 mg (AZD9567 20 mg p<0·0001, 40 mg p=0·0001, 80 mg p=0·0001, and 125 mg p=0·0237). INTERPRETATION: AZD9567 appears to be safe and well tolerated in healthy, predominantly white male volunteers and shows promising initial evidence for improved post-prandial glucose control. Studies of longer duration, with a greater proportion of women and other ethnic groups, and in patients requiring anti-inflammatory treatment are needed to characterise the clinical efficacy and safety profile of AZD9567. FUNDING: AstraZeneca.

Exact Gradients Improve Parameter Estimation in Nonlinear Mixed Effects Models with Stochastic Dynamics.

Nonlinear mixed effects (NLME) modeling based on stochastic differential equations (SDEs) have evolved into a promising approach for analysis of PK/PD data. SDE-NLME models go beyond the realm of standard population modeling as they consider stochastic dynamics, thereby introducing a probabilistic perspective on the state variables. This article presents a summary of the main contributions to SDE-NLME models found in the literature. The aims of this work were to develop an exact gradient version of the first-order conditional estimation (FOCE) method for SDE-NLME models and to investigate whether it enabled faster estimation and better gradient precision/accuracy compared to the use of gradients approximated by finite differences. A simulation-estimation study was set up whereby finite difference approximations of the gradients of each level were interchanged with the exact gradients. Following previous work, the uncertainty of the state variables was accounted for using the extended Kalman filter (EKF). The exact gradient FOCE method was implemented in Mathematica 11 and evaluated on SDE versions of three common PK/PD models. When finite difference gradients were replaced by exact gradients at both FOCE levels, relative runtimes improved between 6- and 32-fold, depending on model complexity. Additionally, gradient precision/accuracy was significantly better in the exact gradient case. We conclude that parameter estimation using FOCE with exact gradients can successfully be applied to SDE-NLME models.

Mixed Effects Modeling Using Stochastic Differential Equations: Illustrated by Pharmacokinetic Data of Nicotinic Acid in Obese Zucker Rats.

Inclusion of stochastic differential equations in mixed effects models provides means to quantify and distinguish three sources of variability in data. In addition to the two commonly encountered sources, measurement error and interindividual variability, we also consider uncertainty in the dynamical model itself. To this end, we extend the ordinary differential equation setting used in nonlinear mixed effects models to include stochastic differential equations. The approximate population likelihood is derived using the first-order conditional estimation with interaction method and extended Kalman filtering. To illustrate the application of the stochastic differential mixed effects model, two pharmacokinetic models are considered. First, we use a stochastic one-compartmental model with first-order input and nonlinear elimination to generate synthetic data in a simulated study. We show that by using the proposed method, the three sources of variability can be successfully separated. If the stochastic part is neglected, the parameter estimates become biased, and the measurement error variance is significantly overestimated. Second, we consider an extension to a stochastic pharmacokinetic model in a preclinical study of nicotinic acid kinetics in obese Zucker rats. The parameter estimates are compared between a deterministic and a stochastic NiAc disposition model, respectively. Discrepancies between model predictions and observations, previously described as measurement noise only, are now separated into a comparatively lower level of measurement noise and a significant uncertainty in model dynamics. These examples demonstrate that stochastic differential mixed effects models are useful tools for identifying incomplete or inaccurate model dynamics and for reducing potential bias in parameter estimates due to such model deficiencies.

Stochastic differential equations as a tool to regularize the parameter estimation problem for continuous time dynamical systems given discrete time measurements.

In this paper we consider the problem of estimating parameters in ordinary differential equations given discrete time experimental data. The impact of going from an ordinary to a stochastic differential equation setting is investigated as a tool to overcome the problem of local minima in the objective function. Using two different models, it is demonstrated that by allowing noise in the underlying model itself, the objective functions to be minimized in the parameter estimation procedures are regularized in the sense that the number of local minima is reduced and better convergence is achieved. The advantage of using stochastic differential equations is that the actual states in the model are predicted from data and this will allow the prediction to stay close to data even when the parameters in the model is incorrect. The extended Kalman filter is used as a state estimator and sensitivity equations are provided to give an accurate calculation of the gradient of the objective function. The method is illustrated using in silico data from the FitzHugh-Nagumo model for excitable media and the Lotka-Volterra predator-prey system. The proposed method performs well on the models considered, and is able to regularize the objective function in both models. This leads to parameter estimation problems with fewer local minima which can be solved by efficient gradient-based methods.

Joint feedback analysis modeling of nonesterified fatty acids in obese Zucker rats and normal Sprague-Dawley rats after different routes of administration of nicotinic acid.

Data were pooled from several studies on nicotinic acid (NiAc) intervention of fatty acid turnover in normal Sprague-Dawley and obese Zucker rats in order to perform a joint PKPD of data from more than 100 normal Sprague-Dawley and obese Zucker rats, exposed to several administration routes and rates. To describe the difference in pharmacodynamic parameters between obese and normal rats, we modified a previously published nonlinear mixed effects model describing tolerance and oscillatory rebound effects of NiAc on nonesterified fatty acids plasma concentrations. An important conclusion is that planning of experiments and dose scheduling cannot rely on pilot studies on normal animals alone. The obese rats have a less-pronounced concentration-response relationship and need higher doses to exhibit desired response. The relative level of fatty acid rebound after cessation of NiAc administration was also quantified in the two rat populations. Building joint normal-disease models with scaling parameter(s) to characterize the "degree of disease" can be a useful tool when designing informative experiments on diseased animals, particularly in the preclinical screen. Data were analyzed using nonlinear mixed effects modeling, for the optimization, we used an improved method for calculating the gradient than the usually adopted finite difference approximation.